DTRCON(l) ) DTRCON(l)NAME
DTRCON - estimate the reciprocal of the condition number of a triangu‐
lar matrix A, in either the 1-norm or the infinity-norm
SYNOPSIS
SUBROUTINE DTRCON( NORM, UPLO, DIAG, N, A, LDA, RCOND, WORK, IWORK,
INFO )
CHARACTER DIAG, NORM, UPLO
INTEGER INFO, LDA, N
DOUBLE PRECISION RCOND
INTEGER IWORK( * )
DOUBLE PRECISION A( LDA, * ), WORK( * )
PURPOSE
DTRCON estimates the reciprocal of the condition number of a triangular
matrix A, in either the 1-norm or the infinity-norm. The norm of A is
computed and an estimate is obtained for norm(inv(A)), then the recip‐
rocal of the condition number is computed as
RCOND = 1 / ( norm(A) * norm(inv(A)) ).
ARGUMENTS
NORM (input) CHARACTER*1
Specifies whether the 1-norm condition number or the infinity-
norm condition number is required:
= '1' or 'O': 1-norm;
= 'I': Infinity-norm.
UPLO (input) CHARACTER*1
= 'U': A is upper triangular;
= 'L': A is lower triangular.
DIAG (input) CHARACTER*1
= 'N': A is non-unit triangular;
= 'U': A is unit triangular.
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input) DOUBLE PRECISION array, dimension (LDA,N)
The triangular matrix A. If UPLO = 'U', the leading N-by-N
upper triangular part of the array A contains the upper trian‐
gular matrix, and the strictly lower triangular part of A is
not referenced. If UPLO = 'L', the leading N-by-N lower trian‐
gular part of the array A contains the lower triangular matrix,
and the strictly upper triangular part of A is not referenced.
If DIAG = 'U', the diagonal elements of A are also not refer‐
enced and are assumed to be 1.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
RCOND (output) DOUBLE PRECISION
The reciprocal of the condition number of the matrix A, com‐
puted as RCOND = 1/(norm(A) * norm(inv(A))).
WORK (workspace) DOUBLE PRECISION array, dimension (3*N)
IWORK (workspace) INTEGER array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
LAPACK version 3.0 15 June 2000 DTRCON(l)
